Critical region of the random bond Ising model

TL;DR

This study uses large-scale simulations to analyze the critical behavior of the 2D Ising model with impurity bonds, revealing impurity-induced changes in magnetic properties and confirming theoretical predictions.

Contribution

It provides high-precision simulation data on impurity effects in the 2D Ising model, clarifying critical exponents and validating theoretical models.

Findings

Magnetization and susceptibility exponents increase with impurities

Critical singularities become sharper due to impurities

Specific heat behavior aligns with Dotsenko-Dotsenko theory

Abstract

We describe results of the cluster algorithm Special Purpose Processor simulations of the 2D Ising model with impurity bonds. Use of large lattices, with the number of spins up to $10^6$, permitted to define critical region of temperatures, where both finite size corrections and corrections to scaling are small. High accuracy data unambiguously show increase of magnetization and magnetic susceptibility effective exponents $\beta$ and $\gamma$, caused by impurities. The $M$ and $\chi$ singularities became more sharp, while the specific heat singularity is smoothed. The specific heat is found to be in a good agreement with Dotsenko-Dotsenko theoretical predictions in the whole critical range of temperatures.